Answer
= $(2 + x)(2 - x)$$(x^{2} + 3)^{\frac{1}{2}}$ [$x^{4} - x^{2} - 13 $]
Work Step by Step
$(x^{2} - 4)(x^{2} + 3)^{\frac{1}{2}}$ - $(x^{2} - 4)^{2}(x^{2} + 3)^{\frac{3}{2}}$
= $(x^{2} - 4)(x^{2} + 3)^{\frac{1}{2}}$ - $(x^{2} - 4)(x^{2} - 4)(x^{2} + 3)^{\frac{1}{2} +1}$
= $(x^{2} - 4)(x^{2} + 3)^{\frac{1}{2}}$[1 - $(x^{2} - 4)(x^{2} + 3)$]
= $(x^{2} - 4)(x^{2} + 3)^{\frac{1}{2}}$ [1 - ($x^{4} - 4x^{2} + 3x^{2} - 12$]
= $(x^{2} - 4)(x^{2} + 3)^{\frac{1}{2}}$ [1 - $x^{4} + 4x^{2} - 3x^{2} + 12$]
= $(x^{2} - 4)(x^{2} + 3)^{\frac{1}{2}}$ [13- $x^{4} + x^{2} $]
= $(4 - x^{2})(x^{2} + 3)^{\frac{1}{2}}$ [$x^{4} - x^{2} - 13 $]
by $(4 - x^{2})$ = $(2 + x)(2 - x)$
$(4 - x^{2})(x^{2} + 3)^{\frac{1}{2}}$ [$x^{4} - x^{2} - 13 $]
= $(2 + x)(2 - x)$$(x^{2} + 3)^{\frac{1}{2}}$ [$x^{4} - x^{2} - 13 $]
